
Population Size: The number of the population in each algorithm is shown in Table 1. In addition, the CA archive size for Two\(\_\) Arch2 is set to 100, as recommended by [1]}.
<TABLE>
Reproduction Operators: The simulated binary crossover operator (SBX) and polynomial mutation are used for reproducing offspring solutions [2]}. The probability of crossover is set to 1.0, and the probability of mutation is set to \(\frac{1}{n}\) , where \(n\)  is the number of variables, and the crossover distribution index \(\eta _c\)  and the mutation distribution index \(\eta _m\)  are both set to 20.0 [3]}, [4]}.

Number of iterations and runs: On each problem, all algorithms are allowed for a maximum of 90\(\,\) 000 fitness evaluations and repeated 20 times independently.

Parameter settings for each algorithm: For SRA3, the parameter \(k\)  in indicator \(I_{\epsilon +}\)  is set to 0.025. For SRA, the parameter \(k\)  in indicator \(I_{\epsilon +}\)  is set to 0.05 and the parameter \(p_c\)  is set to a random number in the range of [0.4,0.6] [5]}. For Two\(\_\) Arch2, the parameter \(k\)  in indicator \(I_{\epsilon +}\)  is set to 0.05, the size of the CA archive, as mentioned above, is set to 100 and the parameter \(p\)  required to calculate the distance is set to \(\frac{1}{m}\) , where \(m\)  is the number of objectives [1]}. For IBEA, the parameter \(k\)  in indicator \(I_{\epsilon +}\)  is set to 0.05 [7]}. For MOEA/D, the number of neighbors is set to \(\lceil {N/10}\rceil \) , where \(N\)  is the size of the population and the maximum replacement number is set to 2 [8]}. Each algorithm set the parameters as suggested in the original papers.

Statistical Test: In order to test the difference between the algorithms, the Wilcoxon's rank sum test with a 0.05 significance level is used for analysis [9]}.

